Precalculus Exponential Functions and the Number e Worksheet (PDF)

Precalculus math worksheet: Exponential Functions and the Number e – Maths PDF

Cover of the book Precalculus Math Worksheets with Answers (PDF)

Download as a PDFThe Precalculus worksheets book with answersPrintable PDFSee the book ›

Sommaire

This exponential practice worksheet for Precalculus covers exponential functions and the number e (Common Core F-LE.A.2, F-IF.C.8b, F-LE.B.5, F-IF.C.7e), with a free PDF to print.

These 20 problems practice exponential functions and the number e (Common Core F-LE.A.2, F-IF.C.8b, F-LE.B.5 and F-IF.C.7e). You will classify growth and decay, write models, graph transformations and use compound interest formulas.

Precalculus · Common Core State Standards: F-LE.A.2, F-IF.C.8b, F-LE.B.5, F-IF.C.7e

Exponential practice worksheet: exercises 1 to 10

Exercise 1 – Growth or decay?

Tell whether each function models growth or decay and give the percent rate: (a) $y=5(1.08)^{x}$; (b) $y=200(0.85)^{x}$.

Exercise 2 – Evaluate

Evaluate $f(x)=3\cdot2^{x}$ at $x=0,\ 1,\ 4$.

Exercise 3 – Equation from two points

Write the exponential function through $(0,5)$ and $(1,15)$.

Exercise 4 – Equation from points two apart

Write the exponential function through $(1,6)$ and $(3,24)$.

Exercise 5 – Town population

A town of $4{,}000$ people grows $3\%$ per year. Write $P(t)$ and find the population after 10 years, rounded to the nearest person.

Exercise 6 – Half-life

A $80$ mg sample loses half its mass every $5$ days. Write $A(t)$ and find the mass after $15$ days.

Exercise 7 – Transformed exponential

Graph of y = 2^(x-1) + 3.

For $y=2^{x-1}+3$ find the asymptote, domain, range and $y$-intercept.

Exercise 8 – Equal bases

Solve $2^{x}=32$.

Exercise 9 – Quarterly compounding

Find the value of $\$2{,}000$ invested at $4\%$ compounded quarterly for 6 years.

Exercise 10 – Compare compounding

Three ways of compounding.

Find the value after 10 years of $\$1{,}000$ at $5\%$ compounded yearly, monthly and continuously.

Exercises 11 and up

Exercise 11 – Continuous growth

Find the value of $\$500$ invested at $3.5\%$ compounded continuously for 8 years.

Exercise 12 – Approach e

Table of (1 + 1/n)^n.

Compute $\left(1+\frac{1}{100}\right)^{100}$ and compare it with $e\approx2.71828$.

Exercise 13 – Bacteria

A culture of 500 bacteria triples every 4 hours: $N(t)=500\cdot3^{t/4}$. Find $N(12)$ and the time when $N=1{,}500$.

Exercise 14 – Car depreciation

A car worth $\$22{,}000$ loses $12\%$ of its value each year. Write $V(t)$ and find its value after 3 years.

Exercise 15 – Equation from a graph

Exponential graph through three points.

The graph passes through $(0,3)$, $(1,6)$ and $(2,12)$. Write its equation and find $f(5)$.

Exercise 16 – Linear versus exponential

Plan A (exponential) and Plan B (linear).

Compare $f(x)=100(1.5)^{x}$ and $g(x)=100+60x$ for $x=1,2,3,4$. After which $x$ does $f$ stay above $g$?

Exercise 17 – Constant percent growth

A club grows from $1{,}200$ to $1{,}728$ members in 2 years with the same percent growth each year. Find the yearly growth rate.

Exercise 18 – Find the principal

After 3 years at $6\%$ compounded yearly, an account holds $\$1{,}191.02$. Find the amount originally deposited.

Exercise 19 – Doubling time

At $7\%$ interest compounded yearly, how many whole years does it take for an investment to at least double?

Exercise 20 – Cooling coffee

Temperature of Maya’s coffee.

Maya’s coffee cools as $T(t)=70+110(0.9)^{t}$ degrees Fahrenheit after $t$ minutes. Find the starting temperature, the temperature after 5 minutes to the nearest tenth, and the temperature the coffee approaches.

Key facts behind this exponential practice worksheet

Key facts

f(x) = a b^x: a = f(0) and b = growth or decay factor.
A rate r per period gives b = 1 + r (growth) or b = 1 – r (decay).
The parent graph has the horizontal asymptote y = 0; y = a b^(x – h) + k has asymptote y = k.
Compound interest: A = P(1 + r/n)^(nt); continuous: A = Pe^(rt).
e is about 2.71828, the limit of (1 + 1/n)^n.

How to use this exponential practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the exponential practice worksheet as a PDF with the button below and keep it with your notes.

All Precalculus chapters: Precalculus math.

Voter.. post

Free printable PDF